How to report ANOVA results in APA format
Reporting ANOVA results correctly in APA 7th edition format requires specific notation: italic statistics, proper degrees of freedom, effect sizes, and — when the omnibus F-test is significant — post-hoc comparisons. This guide provides copy-ready templates for the most common ANOVA designs.
The APA formula for ANOVA
Every ANOVA result in APA format follows the same structure:
F(dfbetween, dfwithin) = [value], p = [value], η2 = [value]
Key formatting rules:
- F is italicized
- Two degrees of freedom are reported: between-groups (numerator) and within-groups (denominator)
- p is italicized, with no leading zero (write .003, not 0.003)
- Effect size (eta-squared or partial eta-squared) is always included
- Round to two decimal places for F and effect sizes; three for p
One-way ANOVA
The most common design: comparing means of 3 or more independent groups on a single factor.
A one-way ANOVA revealed a significant effect of treatment condition on pain reduction, F(2, 87) = 6.42, p = .003, η2 = .13.
A one-way ANOVA found no significant difference in test scores across the three instructional methods, F(2, 57) = 1.24, p = .297, η2 = .04.
Reporting post-hoc comparisons
When the omnibus F-test is significant, report which specific groups differ using post-hoc tests (Tukey's HSD, Bonferroni, or Holm-Šidák correction):
A one-way ANOVA revealed a significant effect of drug dosage on reaction time, F(2, 87) = 6.42, p = .003, η2 = .13. Tukey's post-hoc comparisons indicated that the high-dose group (M = 245 ms, SD = 38) was significantly faster than the placebo group (M = 289 ms, SD = 41), p = .002, d = 1.11. The low-dose group (M = 267 ms, SD = 42) did not differ significantly from either the high-dose (p = .118) or placebo (p = .089) groups.
Two-way (factorial) ANOVA
Reports main effects for each factor and their interaction. Always report the interaction first — if it's significant, main effects should be interpreted cautiously.
A 2 (drug: active vs. placebo) × 3 (time: baseline, 4 weeks, 8 weeks) factorial ANOVA was conducted on pain scores. There was a significant interaction between drug and time, F(2, 174) = 4.58, p = .012, η2p = .05. The main effect of drug was significant, F(1, 87) = 12.31, p < .001, η2p = .12, and the main effect of time was significant, F(2, 174) = 8.76, p < .001, η2p = .09.
Note the subscript p on eta-squared — this denotes partial eta-squared, which is standard for factorial designs because it partials out the variance explained by other factors.
Repeated measures ANOVA
For within-subjects designs. Must report sphericity testing (Mauchly's test) and any corrections applied.
A one-way repeated measures ANOVA showed a significant effect of time point on cortisol levels, F(2, 58) = 9.84, p < .001, η2p = .25. Mauchly's test indicated that sphericity was not violated, χ2(2) = 3.12, p = .210.
A one-way repeated measures ANOVA was conducted on reaction time across four blocks. Mauchly's test indicated that the assumption of sphericity was violated, χ2(5) = 14.56, p = .012. Therefore, Greenhouse-Geisser corrected degrees of freedom were used (ε = .72). The effect of block on reaction time was significant, F(2.16, 64.80) = 5.23, p = .007, η2p = .15.
Common mistake: Forgetting to report the Greenhouse-Geisser epsilon (ε) when sphericity is violated. Reviewers will often ask for this. Note the corrected (non-integer) degrees of freedom in the F result.
Effect size benchmarks for ANOVA
| Effect size | Small | Medium | Large |
|---|---|---|---|
| Eta-squared (η2) | .01 | .06 | .14 |
| Partial eta-squared (η2p) | .01 | .06 | .14 |
| Cohen's f | .10 | .25 | .40 |
These benchmarks (Cohen, 1988) are guidelines, not strict cutoffs. In your field, a "small" effect might be practically important. Always interpret effect sizes in context.
Assumptions to report
Reviewers expect you to document that you checked ANOVA's assumptions. At minimum, mention:
- Normality — Shapiro-Wilk on residuals or per group (see our normality guide)
- Homogeneity of variance — Levene's test (for between-subjects designs)
- Sphericity — Mauchly's test (for repeated measures only)
Normality was assessed via Shapiro-Wilk tests on the residuals (p > .05 for all groups). Levene's test confirmed homogeneity of variances, F(2, 87) = 1.43, p = .245.
When ANOVA assumptions fail
- Normality violated: Use the Kruskal-Wallis H test (for one-way) or Friedman test (for repeated measures)
- Unequal variances: Use Welch's ANOVA (built into many statistical packages)
- Sphericity violated: Apply Greenhouse-Geisser correction (usually automatic)
Quick reference: what to include
| Element | Required? | Example |
|---|---|---|
| F statistic with df | Yes | F(2, 87) = 6.42 |
| p-value | Yes | p = .003 |
| Effect size | Yes (APA 7th ed.) | η2 = .13 |
| Group means and SDs | Yes (in text or table) | M = 23.4, SD = 5.1 |
| Post-hoc comparisons | Yes, if F is significant | Tukey: p = .002 |
| Assumption checks | Recommended | Shapiro-Wilk, Levene's |
Planning an ANOVA study? Use our free sample size calculator to determine how many participants per group you need — select "One-way ANOVA" and enter your expected effect size (Cohen's f).
Join the beta to try this in GraphHelix — run your ANOVA, and get the complete APA-formatted result string with effect sizes, assumption checks, and post-hoc comparisons automatically.
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